text: //=================================================================================================
  /*!
  //  \file blaze/math/expressions/DMatDMatAddExpr.h
  //  \brief Header file for the dense matrix/dense matrix addition expression
  //
  //  Copyright (C) 2013 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_EXPRESSIONS_DMATDMATADDEXPR_H_
  #define _BLAZE_MATH_EXPRESSIONS_DMATDMATADDEXPR_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <iterator>
  #include <blaze/math/Aliases.h>
  #include <blaze/math/constraints/DenseMatrix.h>
  #include <blaze/math/constraints/MatMatAddExpr.h>
  #include <blaze/math/constraints/StorageOrder.h>
  #include <blaze/math/Exception.h>
  #include <blaze/math/expressions/Computation.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/expressions/Forward.h>
  #include <blaze/math/expressions/MatMatAddExpr.h>
  #include <blaze/math/shims/Serial.h>
  #include <blaze/math/SIMD.h>
  #include <blaze/math/traits/AddExprTrait.h>
  #include <blaze/math/traits/AddTrait.h>
  #include <blaze/math/traits/ColumnExprTrait.h>
  #include <blaze/math/traits/RowExprTrait.h>
  #include <blaze/math/traits/SubmatrixExprTrait.h>
  #include <blaze/math/typetraits/Columns.h>
  #include <blaze/math/typetraits/HasSIMDAdd.h>
  #include <blaze/math/typetraits/IsAligned.h>
  #include <blaze/math/typetraits/IsExpression.h>
  #include <blaze/math/typetraits/IsHermitian.h>
  #include <blaze/math/typetraits/IsLower.h>
  #include <blaze/math/typetraits/IsPadded.h>
  #include <blaze/math/typetraits/IsStrictlyLower.h>
  #include <blaze/math/typetraits/IsStrictlyUpper.h>
  #include <blaze/math/typetraits/IsSymmetric.h>
  #include <blaze/math/typetraits/IsTemporary.h>
  #include <blaze/math/typetraits/IsUniLower.h>
  #include <blaze/math/typetraits/IsUniUpper.h>
  #include <blaze/math/typetraits/IsUpper.h>
  #include <blaze/math/typetraits/RequiresEvaluation.h>
  #include <blaze/math/typetraits/Rows.h>
  #include <blaze/system/Inline.h>
  #include <blaze/system/Thresholds.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Reference.h>
  #include <blaze/util/EnableIf.h>
  #include <blaze/util/IntegralConstant.h>
  #include <blaze/util/logging/FunctionTrace.h>
  #include <blaze/util/mpl/And.h>
  #include <blaze/util/mpl/If.h>
  #include <blaze/util/mpl/Max.h>
  #include <blaze/util/mpl/Or.h>
  #include <blaze/util/Types.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS DMATDMATADDEXPR
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Expression object for dense matrix-dense matrix additions.
  // \ingroup dense_matrix_expression
  //
  // The DMatDMatAddExpr class represents the compile time expression for additions between
  // dense matrices with identical storage order.
  */
  template< typename MT1  // Type of the left-hand side dense matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO >     // Storage order
  class DMatDMatAddExpr : public DenseMatrix< DMatDMatAddExpr<MT1,MT2,SO>, SO >
                        , private MatMatAddExpr
                        , private Computation
  {
   private:
     //**Type definitions****************************************************************************
     typedef ResultType_<MT1>     RT1;  //!< Result type of the left-hand side dense matrix expression.
     typedef ResultType_<MT2>     RT2;  //!< Result type of the right-hand side dense matrix expression.
     typedef ReturnType_<MT1>     RN1;  //!< Return type of the left-hand side dense matrix expression.
     typedef ReturnType_<MT2>     RN2;  //!< Return type of the right-hand side dense matrix expression.
     typedef CompositeType_<MT1>  CT1;  //!< Composite type of the left-hand side dense matrix expression.
     typedef CompositeType_<MT2>  CT2;  //!< Composite type of the right-hand side dense matrix expression.
     typedef ElementType_<MT1>    ET1;  //!< Element type of the left-hand side dense matrix expression.
     typedef ElementType_<MT2>    ET2;  //!< Element type of the right-hand side dense matrix expression.
     //**********************************************************************************************
  
     //**Return type evaluation**********************************************************************
     //! Compilation switch for the selection of the subscript operator return type.
     /*! The \a returnExpr compile time constant expression is a compilation switch for the
         selection of the \a ReturnType. If either matrix operand returns a temporary vector
         or matrix, \a returnExpr will be set to \a false and the subscript operator will
         return it's result by value. Otherwise \a returnExpr will be set to \a true and
         the subscript operator may return it's result as an expression. */
     enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
  
     //! Expression return type for the subscript operator.
     typedef AddExprTrait_<RN1,RN2>  ExprReturnType;
     //**********************************************************************************************
  
     //**Serial evaluation strategy******************************************************************
     //! Compilation switch for the serial evaluation strategy of the addition expression.
     /*! The \a useAssign compile time constant expression represents a compilation switch for
         the serial evaluation strategy of the addition expression. In case either of the two
         dense matrix operands requires an intermediate evaluation or the subscript operator
         can only return by value, \a useAssign will be set to 1 and the addition expression
         will be evaluated via the \a assign function family. Otherwise \a useAssign will be
         set to 0 and the expression will be evaluated via the function call operator. */
     enum : bool { useAssign = RequiresEvaluation<MT1>::value || RequiresEvaluation<MT2>::value || !returnExpr };
  
     /*! \cond BLAZE_INTERNAL */
     //! Helper structure for the explicit application of the SFINAE principle.
     template< typename MT >
     struct UseAssign {
        enum : bool { value = useAssign };
     };
     /*! \endcond */
     //**********************************************************************************************
  
     //**Parallel evaluation strategy****************************************************************
     /*! \cond BLAZE_INTERNAL */
     //! Helper structure for the explicit application of the SFINAE principle.
     /*! The UseSMPAssign struct is a helper struct for the selection of the parallel evaluation
         strategy. In case at least one of the two matrix operands is not SMP assignable and at
         least one of the two operands requires an intermediate evaluation, \a value is set to 1
         and the expression specific evaluation strategy is selected. Otherwise \a value is set
         to 0 and the default strategy is chosen. */
     template< typename MT >
     struct UseSMPAssign {
        enum : bool { value = ( !MT1::smpAssignable || !MT2::smpAssignable ) && useAssign };
     };
     /*! \endcond */
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     typedef DMatDMatAddExpr<MT1,MT2,SO>  This;           //!< Type of this DMatDMatAdd instance.
     typedef AddTrait_<RT1,RT2>           ResultType;     //!< Result type for expression template evaluations.
     typedef OppositeType_<ResultType>    OppositeType;   //!< Result type with opposite storage order for expression template evaluations.
     typedef TransposeType_<ResultType>   TransposeType;  //!< Transpose type for expression template evaluations.
     typedef ElementType_<ResultType>     ElementType;    //!< Resulting element type.
  
     //! Return type for expression template evaluations.
     typedef const IfTrue_< returnExpr, ExprReturnType, ElementType >  ReturnType;
  
     //! Data type for composite expression templates.
     typedef IfTrue_< useAssign, const ResultType, const DMatDMatAddExpr& >  CompositeType;
  
     //! Composite type of the left-hand side dense matrix expression.
     typedef If_< IsExpression<MT1>, const MT1, const MT1& >  LeftOperand;
  
     //! Composite type of the right-hand side dense matrix expression.
     typedef If_< IsExpression<MT2>, const MT2, const MT2& >  RightOperand;
     //**********************************************************************************************
  
     //**ConstIterator class definition**************************************************************
     /*!\brief Iterator over the elements of the dense matrix.
     */
     class ConstIterator
     {
      public:
        //**Type definitions*************************************************************************
        typedef std::random_access_iterator_tag  IteratorCategory;  //!< The iterator category.
        typedef ElementType                      ValueType;         //!< Type of the underlying elements.
        typedef ElementType*                     PointerType;       //!< Pointer return type.
        typedef ElementType&                     ReferenceType;     //!< Reference return type.
        typedef ptrdiff_t                        DifferenceType;    //!< Difference between two iterators.
  
        // STL iterator requirements
        typedef IteratorCategory  iterator_category;  //!< The iterator category.
        typedef ValueType         value_type;         //!< Type of the underlying elements.
        typedef PointerType       pointer;            //!< Pointer return type.
        typedef ReferenceType     reference;          //!< Reference return type.
        typedef DifferenceType    difference_type;    //!< Difference between two iterators.
  
        //! ConstIterator type of the left-hand side dense matrix expression.
        typedef ConstIterator_<MT1>  LeftIteratorType;
  
        //! ConstIterator type of the right-hand side dense matrix expression.
        typedef ConstIterator_<MT2>  RightIteratorType;
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Constructor for the ConstIterator class.
        //
        // \param left Iterator to the initial left-hand side element.
        // \param right Iterator to the initial right-hand side element.
        */
        explicit inline ConstIterator( LeftIteratorType left, RightIteratorType right )
           : left_ ( left  )  // Iterator to the current left-hand side element
           , right_( right )  // Iterator to the current right-hand side element
        {}
        //*******************************************************************************************
  
        //**Addition assignment operator*************************************************************
        /*!\brief Addition assignment operator.
        //
        // \param inc The increment of the iterator.
        // \return The incremented iterator.
        */
        inline ConstIterator& operator+=( size_t inc ) {
           left_  += inc;
           right_ += inc;
           return *this;
        }
        //*******************************************************************************************
  
        //**Subtraction assignment operator**********************************************************
        /*!\brief Subtraction assignment operator.
        //
        // \param dec The decrement of the iterator.
        // \return The decremented iterator.
        */
        inline ConstIterator& operator-=( size_t dec ) {
           left_  -= dec;
           right_ -= dec;
           return *this;
        }
        //*******************************************************************************************
  
        //**Prefix increment operator****************************************************************
        /*!\brief Pre-increment operator.
        //
        // \return Reference to the incremented iterator.
        */
        inline ConstIterator& operator++() {
           ++left_;
           ++right_;
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix increment operator***************************************************************
        /*!\brief Post-increment operator.
        //
        // \return The previous position of the iterator.
        */
        inline const ConstIterator operator++( int ) {
           return ConstIterator( left_++, right_++ );
        }
        //*******************************************************************************************
  
        //**Prefix decrement operator****************************************************************
        /*!\brief Pre-decrement operator.
        //
        // \return Reference to the decremented iterator.
        */
        inline ConstIterator& operator--() {
           --left_;
           --right_;
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix decrement operator***************************************************************
        /*!\brief Post-decrement operator.
        //
        // \return The previous position of the iterator.
        */
        inline const ConstIterator operator--( int ) {
           return ConstIterator( left_--, right_-- );
        }
        //*******************************************************************************************
  
        //**Element access operator******************************************************************
        /*!\brief Direct access to the element at the current iterator position.
        //
        // \return The resulting value.
        */
        inline ReturnType operator*() const {
           return (*left_) + (*right_);
        }
        //*******************************************************************************************
  
        //**Load function****************************************************************************
        /*!\brief Access to the SIMD elements of the matrix.
        //
        // \return The resulting SIMD element.
        */
        inline auto load() const noexcept {
           return left_.load() + right_.load();
        }
        //*******************************************************************************************
  
        //**Equality operator************************************************************************
        /*!\brief Equality comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators refer to the same element, \a false if not.
        */
        inline bool operator==( const ConstIterator& rhs ) const {
           return left_ == rhs.left_;
        }
        //*******************************************************************************************
  
        //**Inequality operator**********************************************************************
        /*!\brief Inequality comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators don't refer to the same element, \a false if they do.
        */
        inline bool operator!=( const ConstIterator& rhs ) const {
           return left_ != rhs.left_;
        }
        //*******************************************************************************************
  
        //**Less-than operator***********************************************************************
        /*!\brief Less-than comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller, \a false if not.
        */
        inline bool operator<( const ConstIterator& rhs ) const {
           return left_ < rhs.left_;
        }
        //*******************************************************************************************
  
        //**Greater-than operator********************************************************************
        /*!\brief Greater-than comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater, \a false if not.
        */
        inline bool operator>( const ConstIterator& rhs ) const {
           return left_ > rhs.left_;
        }
        //*******************************************************************************************
  
        //**Less-or-equal-than operator**************************************************************
        /*!\brief Less-than comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller or equal, \a false if not.
        */
        inline bool operator<=( const ConstIterator& rhs ) const {
           return left_ <= rhs.left_;
        }
        //*******************************************************************************************
  
        //**Greater-or-equal-than operator***********************************************************
        /*!\brief Greater-than comparison between two ConstIterator objects.
        //
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater or equal, \a false if not.
        */
        inline bool operator>=( const ConstIterator& rhs ) const {
           return left_ >= rhs.left_;
        }
        //*******************************************************************************************
  
        //**Subtraction operator*********************************************************************
        /*!\brief Calculating the number of elements between two iterators.
        //
        // \param rhs The right-hand side iterator.
        // \return The number of elements between the two iterators.
        */
        inline DifferenceType operator-( const ConstIterator& rhs ) const {
           return left_ - rhs.left_;
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between a ConstIterator and an integral value.
        //
        // \param it The iterator to be incremented.
        // \param inc The number of elements the iterator is incremented.
        // \return The incremented iterator.
        */
        friend inline const ConstIterator operator+( const ConstIterator& it, size_t inc ) {
           return ConstIterator( it.left_ + inc, it.right_ + inc );
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between an integral value and a ConstIterator.
        //
        // \param inc The number of elements the iterator is incremented.
        // \param it The iterator to be incremented.
        // \return The incremented iterator.
        */
        friend inline const ConstIterator operator+( size_t inc, const ConstIterator& it ) {
           return ConstIterator( it.left_ + inc, it.right_ + inc );
        }
        //*******************************************************************************************
  
        //**Subtraction operator*********************************************************************
        /*!\brief Subtraction between a ConstIterator and an integral value.
        //
        // \param it The iterator to be decremented.
        // \param dec The number of elements the iterator is decremented.
        // \return The decremented iterator.
        */
        friend inline const ConstIterator operator-( const ConstIterator& it, size_t dec ) {
           return ConstIterator( it.left_ - dec, it.right_ - dec );
        }
        //*******************************************************************************************
  
      private:
        //**Member variables*************************************************************************
        LeftIteratorType  left_;   //!< Iterator to the current left-hand side element.
        RightIteratorType right_;  //!< Iterator to the current right-hand side element.
        //*******************************************************************************************
     };
     //**********************************************************************************************
  
     //**Compilation flags***************************************************************************
     //! Compilation switch for the expression template evaluation strategy.
     enum : bool { simdEnabled = MT1::simdEnabled && MT2::simdEnabled &&
                                 HasSIMDAdd<ET1,ET2>::value };
  
     //! Compilation switch for the expression template assignment strategy.
     enum : bool { smpAssignable = MT1::smpAssignable && MT2::smpAssignable };
     //**********************************************************************************************
  
     //**SIMD properties*****************************************************************************
     //! The number of elements packed within a single SIMD element.
     enum : size_t { SIMDSIZE = SIMDTrait<ElementType>::size };
     //**********************************************************************************************
  
     //**Constructor*********************************************************************************
     /*!\brief Constructor for the DMatDMatAddExpr class.
     //
     // \param lhs The left-hand side operand of the addition expression.
     // \param rhs The right-hand side operand of the addition expression.
     */
     explicit inline DMatDMatAddExpr( const MT1& lhs, const MT2& rhs ) noexcept
        : lhs_( lhs )  // Left-hand side dense matrix of the addition expression
        , rhs_( rhs )  // Right-hand side dense matrix of the addition expression
     {
        BLAZE_INTERNAL_ASSERT( lhs.rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
     }
     //**********************************************************************************************
  
     //**Access operator*****************************************************************************
     /*!\brief 2D-access to the matrix elements.
     //
     // \param i Access index for the row. The index has to be in the range \f$[0..M-1]\f$.
     // \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     */
     inline ReturnType operator()( size_t i, size_t j ) const {
        BLAZE_INTERNAL_ASSERT( i < lhs_.rows()   , "Invalid row access index"    );
        BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
        return lhs_(i,j) + rhs_(i,j);
     }
     //**********************************************************************************************
  
     //**At function*********************************************************************************
     /*!\brief Checked access to the matrix elements.
     //
     // \param i Access index for the row. The index has to be in the range \f$[0..M-1]\f$.
     // \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     // \exception std::out_of_range Invalid matrix access index.
     */
     inline ReturnType at( size_t i, size_t j ) const {
        if( i >= lhs_.rows() ) {
           BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
        }
        if( j >= lhs_.columns() ) {
           BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
        }
        return (*this)(i,j);
     }
     //**********************************************************************************************
  
     //**Load function*******************************************************************************
     /*!\brief Access to the SIMD elements of the matrix.
     //
     // \param i Access index for the row. The index has to be in the range \f$[0..M-1]\f$.
     // \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
     // \return Reference to the accessed values.
     */
     BLAZE_ALWAYS_INLINE auto load( size_t i, size_t j ) const noexcept {
        BLAZE_INTERNAL_ASSERT( i < lhs_.rows()   , "Invalid row access index"    );
        BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
        BLAZE_INTERNAL_ASSERT( !SO || ( i % SIMDSIZE == 0UL ), "Invalid row access index"    );
        BLAZE_INTERNAL_ASSERT( SO  || ( j % SIMDSIZE == 0UL ), "Invalid column access index" );
        return lhs_.load(i,j) + rhs_.load(i,j);
     }
     //**********************************************************************************************
  
     //**Begin function******************************************************************************
     /*!\brief Returns an iterator to the first non-zero element of row \a i.
     //
     // \param i The row index.
     // \return Iterator to the first non-zero element of row \a i.
     */
     inline ConstIterator begin( size_t i ) const {
        return ConstIterator( lhs_.begin(i), rhs_.begin(i) );
     }
     //**********************************************************************************************
  
     //**End function********************************************************************************
     /*!\brief Returns an iterator just past the last non-zero element of row \a i.
     //
     // \param i The row index.
     // \return Iterator just past the last non-zero element of row \a i.
     */
     inline ConstIterator end( size_t i ) const {
        return ConstIterator( lhs_.end(i), rhs_.end(i) );
     }
     //**********************************************************************************************
  
     //**Rows function*******************************************************************************
     /*!\brief Returns the current number of rows of the matrix.
     //
     // \return The number of rows of the matrix.
     */
     inline size_t rows() const noexcept {
        return lhs_.rows();
     }
     //**********************************************************************************************
  
     //**Columns function****************************************************************************
     /*!\brief Returns the current number of columns of the matrix.
     //
     // \return The number of columns of the matrix.
     */
     inline size_t columns() const noexcept {
        return lhs_.columns();
     }
     //**********************************************************************************************
  
     //**Left operand access*************************************************************************
     /*!\brief Returns the left-hand side dense matrix operand.
     //
     // \return The left-hand side dense matrix operand.
     */
     inline LeftOperand leftOperand() const noexcept {
        return lhs_;
     }
     //**********************************************************************************************
  
     //**Right operand access************************************************************************
     /*!\brief Returns the right-hand side dense matrix operand.
     //
     // \return The right-hand side dense matrix operand.
     */
     inline RightOperand rightOperand() const noexcept {
        return rhs_;
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the expression can alias with the given address \a alias.
     //
     // \param alias The alias to be checked.
     // \return \a true in case the expression can alias, \a false otherwise.
     */
     template< typename T >
     inline bool canAlias( const T* alias ) const noexcept {
        return ( IsExpression<MT1>::value && ( RequiresEvaluation<MT1>::value ? lhs_.isAliased( alias ) : lhs_.canAlias( alias ) ) ) ||
               ( IsExpression<MT2>::value && ( RequiresEvaluation<MT2>::value ? rhs_.isAliased( alias ) : rhs_.canAlias( alias ) ) );
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the expression is aliased with the given address \a alias.
     //
     // \param alias The alias to be checked.
     // \return \a true in case an alias effect is detected, \a false otherwise.
     */
     template< typename T >
     inline bool isAliased( const T* alias ) const noexcept {
        return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the operands of the expression are properly aligned in memory.
     //
     // \return \a true in case the operands are aligned, \a false if not.
     */
     inline bool isAligned() const noexcept {
        return lhs_.isAligned() && rhs_.isAligned();
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the expression can be used in SMP assignments.
     //
     // \return \a true in case the expression can be used in SMP assignments, \a false if not.
     */
     inline bool canSMPAssign() const noexcept {
        return lhs_.canSMPAssign() || rhs_.canSMPAssign() ||
               ( ( ( SO == rowMajor ) ? rows() : columns() ) > SMP_DMATDMATADD_THRESHOLD );
     }
     //**********************************************************************************************
  
   private:
     //**Member variables****************************************************************************
     LeftOperand  lhs_;  //!< Left-hand side dense matrix of the addition expression.
     RightOperand rhs_;  //!< Right-hand side dense matrix of the addition expression.
     //**********************************************************************************************
  
     //**Assignment to dense matrices****************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a dense matrix-dense
     // matrix addition expression to a dense matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case either
     // of the two operands requires an intermediate evaluation.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseAssign<MT> >
        assign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        if( !IsExpression<MT1>::value && isSame( ~lhs, rhs.lhs_ ) ) {
           addAssign( ~lhs, rhs.rhs_ );
        }
        else if( !IsExpression<MT2>::value && isSame( ~lhs, rhs.rhs_ ) ) {
           addAssign( ~lhs, rhs.lhs_ );
        }
        else {
           assign   ( ~lhs, rhs.lhs_ );
           addAssign( ~lhs, rhs.rhs_ );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Assignment to sparse matrices***************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a dense matrix-dense matrix addition to a sparse matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side sparse matrix.
     // \param rhs The right-hand side addition expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a dense matrix-dense
     // matrix addition expression to a sparse matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case either
     // of the two operands requires an intermediate evaluation.
     */
     template< typename MT  // Type of the target sparse matrix
             , bool SO2 >   // Storage order of the target sparse matrix
     friend inline EnableIf_< UseAssign<MT> >
        assign( SparseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        typedef IfTrue_< SO == SO2, ResultType, OppositeType >  TmpType;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( OppositeType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OppositeType, !SO );
        BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT, TmpType );
        BLAZE_CONSTRAINT_MUST_BE_REFERENCE_TYPE( CompositeType_<TmpType> );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const TmpType tmp( serial( rhs ) );
        assign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to dense matrices*******************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Addition assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be added.
     // \return void
     //
     // This function implements the performance optimized addition assignment of a dense matrix-
     // dense matrix addition expression to a dense matrix. Due to the explicit application of
     // the SFINAE principle, this function can only be selected by the compiler in case either
     // of the operands requires an intermediate evaluation.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseAssign<MT> >
        addAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        addAssign( ~lhs, rhs.lhs_ );
        addAssign( ~lhs, rhs.rhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to sparse matrices******************************************************
     // No special implementation for the addition assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Subtraction assignment to dense matrices****************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Subtraction assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be subtracted.
     // \return void
     //
     // This function implements the performance optimized subtraction assignment of a dense matrix-
     // dense matrix addition expression to a dense matrix. Due to the explicit application of
     // the SFINAE principle, this function can only be selected by the compiler in case either
     // of the operands requires an intermediate evaluation.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseAssign<MT> >
        subAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        subAssign( ~lhs, rhs.lhs_ );
        subAssign( ~lhs, rhs.rhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Subtraction assignment to sparse matrices***************************************************
     // No special implementation for the subtraction assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Multiplication assignment to dense matrices*************************************************
     // No special implementation for the multiplication assignment to dense matrices.
     //**********************************************************************************************
  
     //**Multiplication assignment to sparse matrices************************************************
     // No special implementation for the multiplication assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP assignment to dense matrices************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized SMP assignment of a dense matrix-dense
     // matrix addition expression to a dense matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case the expression
     // specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        if( !IsExpression<MT1>::value && isSame( ~lhs, rhs.lhs_ ) ) {
           smpAddAssign( ~lhs, rhs.rhs_ );
        }
        else if( !IsExpression<MT2>::value && isSame( ~lhs, rhs.rhs_ ) ) {
           smpAddAssign( ~lhs, rhs.lhs_ );
        }
        else {
           smpAssign   ( ~lhs, rhs.lhs_ );
           smpAddAssign( ~lhs, rhs.rhs_ );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP assignment to sparse matrices***********************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP assignment of a dense matrix-dense matrix addition to a sparse matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side sparse matrix.
     // \param rhs The right-hand side addition expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized SMP assignment of a dense matrix-dense
     // matrix addition expression to a sparse matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case the expression
     // specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target sparse matrix
             , bool SO2 >   // Storage order of the target sparse matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAssign( SparseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        typedef IfTrue_< SO == SO2, ResultType, OppositeType >  TmpType;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( OppositeType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OppositeType, !SO );
        BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT, TmpType );
        BLAZE_CONSTRAINT_MUST_BE_REFERENCE_TYPE( CompositeType_<TmpType> );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const TmpType tmp( rhs );
        smpAssign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP addition assignment to dense matrices***************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP addition assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be added.
     // \return void
     //
     // This function implements the performance optimized SMP addition assignment of a dense
     // matrix-dense matrix addition expression to a dense matrix. Due to the explicit application
     // of the SFINAE principle, this function can only be selected by the compiler in case the
     // expression specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAddAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        smpAddAssign( ~lhs, rhs.lhs_ );
        smpAddAssign( ~lhs, rhs.rhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP addition assignment to sparse matrices**************************************************
     // No special implementation for the SMP addition assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP subtraction assignment to dense matrices************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP subtraction assignment of a dense matrix-dense matrix addition to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side addition expression to be subtracted.
     // \return void
     //
     // This function implements the performance SMP optimized subtraction assignment of a dense
     // matrix-dense matrix addition expression to a dense matrix. Due to the explicit application
     // of the SFINAE principle, this function can only be selected by the compiler in case the
     // expression specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpSubAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatAddExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        smpSubAssign( ~lhs, rhs.lhs_ );
        smpSubAssign( ~lhs, rhs.rhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP subtraction assignment to sparse matrices***********************************************
     // No special implementation for the SMP subtraction assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP multiplication assignment to dense matrices*********************************************
     // No special implementation for the SMP multiplication assignment to dense matrices.
     //**********************************************************************************************
  
     //**SMP multiplication assignment to sparse matrices********************************************
     // No special implementation for the SMP multiplication assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     /*! \cond BLAZE_INTERNAL */
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( MT2 );
     BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT1, MT2 );
     BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATADDEXPR( MT1, MT2 );
     /*! \endcond */
     //**********************************************************************************************
  };
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  GLOBAL BINARY ARITHMETIC OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Addition operator for the addition of two dense matrices with identical storage order
  //        (\f$ A=B+C \f$).
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the matrix addition.
  // \param rhs The right-hand side dense matrix to be added to the left-hand side matrix.
  // \return The sum of the two matrices.
  // \exception std::invalid_argument Matrix sizes do not match
  //
  // This operator represents the addition of two dense matrices with identical storage order:
  
     \code
     using blaze::rowMajor;
  
     blaze::DynamicMatrix<double,rowMajor> A, B, C;
     // ... Resizing and initialization
     C = A + B;
     \endcode
  
  // The operator returns an expression representing a dense matrix of the higher-order element
  // type of the two involved matrix element types \a T1::ElementType and \a T2::ElementType.
  // Both matrix types \a T1 and \a T2 as well as the two element types \a T1::ElementType and
  // \a T2::ElementType have to be supported by the AddTrait class template.\n
  // In case the current number of rows and columns of the two given matrices don't match, a
  // \a std::invalid_argument is thrown.
  */
  template< typename T1  // Type of the left-hand side dense matrix
          , typename T2  // Type of the right-hand side dense matrix
          , bool SO >    // Storage order
  inline const DMatDMatAddExpr<T1,T2,SO>
     operator+( const DenseMatrix<T1,SO>& lhs, const DenseMatrix<T2,SO>& rhs )
  {
     BLAZE_FUNCTION_TRACE;
  
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
     }
  
     return DMatDMatAddExpr<T1,T2,SO>( ~lhs, ~rhs );
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ROWS SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct Rows< DMatDMatAddExpr<MT1,MT2,SO> >
     : public Max< Rows<MT1>, Rows<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  COLUMNS SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct Columns< DMatDMatAddExpr<MT1,MT2,SO> >
     : public Max< Columns<MT1>, Columns<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISALIGNED SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsAligned< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsAligned<MT1>, IsAligned<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISPADDED SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsPadded< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsPadded<MT1>, IsPadded<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSYMMETRIC SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsSymmetric< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< IsSymmetric<MT1>::value && IsSymmetric<MT2>::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISHERMITIAN SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsHermitian< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< IsHermitian<MT1>::value && IsHermitian<MT2>::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISLOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsLower< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsLower<MT1>, IsLower<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUNILOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUniLower< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< Or< And< IsUniLower<MT1>, IsStrictlyLower<MT2> >
                              , And< IsUniLower<MT2>, IsStrictlyLower<MT1> > >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSTRICTLYLOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsStrictlyLower< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUpper< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsUpper<MT1>, IsUpper<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUNIUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUniUpper< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< Or< And< IsUniUpper<MT1>, IsStrictlyUpper<MT2> >
                              , And< IsUniUpper<MT2>, IsStrictlyUpper<MT1> > >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSTRICTLYUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsStrictlyUpper< DMatDMatAddExpr<MT1,MT2,SO> >
     : public BoolConstant< And< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >::value >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  EXPRESSION TRAIT SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO, bool AF >
  struct SubmatrixExprTrait< DMatDMatAddExpr<MT1,MT2,SO>, AF >
  {
   public:
     //**********************************************************************************************
     using Type = AddExprTrait_< SubmatrixExprTrait_<const MT1,AF>
                               , SubmatrixExprTrait_<const MT2,AF> >;
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct RowExprTrait< DMatDMatAddExpr<MT1,MT2,SO> >
  {
   public:
     //**********************************************************************************************
     using Type = AddExprTrait_< RowExprTrait_<const MT1>
                               , RowExprTrait_<const MT2> >;
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct ColumnExprTrait< DMatDMatAddExpr<MT1,MT2,SO> >
  {
   public:
     //**********************************************************************************************
     using Type = AddExprTrait_< ColumnExprTrait_<const MT1>
                               , ColumnExprTrait_<const MT2> >;
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  